It was on January 2, 1981 that the man who had brutally murdered 13 women was finally snared - although it would be several days before the driver who had been arrested in Melbourne Avenue, Broomhill would be revealed as the deadly serial killer who had struck fear into northern England for years.
Sutcliffe was found in a car in the tree-lined and gloomy road with 24-year-old prostitute Olivia Reivers. At the time, the area was deep in the city's red light district - and a known haunt for prostitutes and their clients.
The pair were parked in the drive way of Light Trades House when two Sheffield officers, Sgt Bob Ring and the inexperienced probationer PC Robert Hydes decided to investigate.
A police check revealed his car had false number plates and Sutcliffe was arrested and taken to Hammerton Road police station before being transferred to Dewsbury Police Station.
At Dewsbury he was questioned in relation to the Yorkshire Ripper case as he matched many of the known physical characteristics.
The next day, Sgt Ring returned to the scene of the arrest and discovered a knife, hammer and rope he had discarded when he briefly slipped away from the police after telling them he was "bursting for a pee".
Sutcliffe hid a second knife in the toilet cistern at the police station when he was permitted to use the toilet. The police obtained a search warrant for his home at 6, Garden Lane in Heaton, Bradford and brought his wife in for questioning.
When Sutcliffe was stripped at the police station he was wearing an inverted V-neck sweater under his trousers. The sleeves had been pulled over his legs and the V-neck exposed his genital area.
The front of the elbows were padded to protect his knees as, presumably, he knelt over his victims' corpses.
After two days of intensive questioning, on the afternoon of 4 January 1981 Sutcliffe suddenly declared he was the Ripper.
Over the next day, Sutcliffe calmly described his many attacks and at his trial, he pleaded not guilty to 13 charges of murder, but guilty to manslaughter on the grounds of diminished responsibility. The basis of his defence was he claimed to be the tool of God's will.
Sutcliffe claimed to have heard voices that ordered him to kill prostitutes while working as a gravedigger.
Sutcliffe had regularly used the services of prostitutes in Leeds and Bradford and his outbreak of violence towards them seems to have occurred because he was swindled out of money by a prostitute and her pimp.
Carrying out his murder spree over five years, his first killing was in 1975 - but he had carried out a number of other attacks before then.
The trial lasted two weeks and Sutcliffe was found guilty of murder on all 13 counts and attempting to murder seven others and was sentenced to twenty concurrent sentences of life imprisonment.
On 16 July 2010, the High Court issued Sutcliffe with a whole life tariff, meaning he is unlikely ever to be released.